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Table 1

Comparison of the mean lensing optical depth and the expected number of detected multiply imaged quasars for different values of the survey angular resolution corresponding to a perfect survey (θmin = 0′′), Gaia (θmin = 0.2′′), and typical ground-based observations (θmin = 0.6′′).

Survey NQSO θmin = 0′′ θmin = 0.2′′ θmin = 0.6′′
Early-type galaxies

SIS SIE SIS SIE SIS SIE

τ 3.994 × 10-3 3.747 × 10-3 3.917 × 10-3 3.663 × 10-3 2.718 × 10-3 2.431 × 10-3
τ2⟩ / ⟨τ 0.917 0.92 0.948
τ3⟩ / ⟨τ 1.15 × 10-3 2.564 × 10-2 4.614 × 10-2
τ4⟩ / ⟨τ 8.205 × 10-2 5.25 × 10-2 5.59 × 10-3

This study 6.64465 × 105 2653 2490 2602 2433 1806 1615
Three images 3 62 75
Four images 204 134 9
Late-type galaxies

SIS SIE SIS SIE SIS SIE

τ 1.278 × 10-3 1.141 × 10-3 8.404 × 10-4 6.815 × 10-4
τ2⟩ / ⟨τ 0.8413 0.92
τ3⟩ / ⟨τ 0.01206 0.07244
τ4⟩ / ⟨τ 0.1466 0.05192

This study 6.64465 × 105 849 758 558 453
Three images 9 33
Four images 111 24
All deflectors (early- and late-type galaxies)

SIS SIE SIS SIE SIS SIE

This study 6.64465 × 105 3502 3248 3160 2886 1806 1615
> two images 327 253 84

Mignard (2012) 5.5−7 × 105
Slezak (2007) 7.2 × 105

Notes. For each value of θmin, the table displays the average lensing optical depth τ for both the SIS and SIE cases. In the latter case, the fraction of lensing events as a function of the number i of lensed images detected is also displayed τi⟩ / ⟨τ. The bottom part of the table indicates the expected number of lenses in the survey, the total number, and the number of events with a given number of detected lensed images. For comparison, we report the expected number of lensing events considering the population of sources found in Mignard (2012) and Slezak (2007), assuming that these sources have a similar distribution in the redshift-absolute magnitude diagram.

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